Random Graph Connectivity - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: probability, graph-theory, erdos-renyi, threshold
Problem Description
Consider an Erdős–Rényi random graph $G(n, p)$ where $n$ represents the number of vertices and $p$ represents the probability of an edge existing between any two vertices. You are tasked with determining the sharp threshold for $p$ at which the graph becomes almost surely connected as $n$ approaches infinity. This means you need to find the smallest value of $p$ such that the probability of the graph being connected approaches 1 as $n$ grows large.
What is the sharp threshold for $p$ at which th
Practice this hard trader interview question on MyntBit - the all-in-one quant learning platform with 200+ quant interview questions for Jane Street, Citadel, Two Sigma, and other top quantitative finance firms.